If P = (x3 + y3)/((x - y)2 + 3xy) , Q =( (x + y)2 - 3xy)/(x3 - y3) and R = ((x + y)2 + (x - y)2)/(x2 - y2)) , then what is the value of (P ÷ Q) × R ?
Show answer & explanation
Correct answer: B
Explanation
The correct answer is option 2 i.e 2(x2 + y2)
We will simplify each term one by one.
P = (x3 + y3)/((x - y)2 + 3xy) = (x + y)(x2 + y2 - xy) / x2 + y2 + xy
Q = ( (x + y)2 - 3xy)/(x3 - y3) = x2 + y2 - xy / (x - y)(x2 + y2 + xy)
R = ((x + y)2 + (x - y)2)/(x2 - y2)) = 2(x2 + y2) / (x2 - y2)
⇒ P / Q = [(x + y)(x2 + y2 - xy) / x2 + y2 + xy / x2 + y2 - xy / (x - y)(x2 + y2 + xy)]
⇒ (x + y)(x - y) = x2 - y2
⇒ (P / Q) × R = (x2 - y2) × 2(x2 + y2) / (x2 - y2) = 2(x2 + y2)